NEW DELHI—An already-bitter battle between Uber Technologies Inc. and its main local competitor for dominance of the Indian market has hit a new level of ferocity.

Uber earlier this week filed a lawsuit against Bangalore-based ANI Technologies Pvt. Ltd., which owns Ola, accusing the rival ride-sharing company of, among other things, creating tens of thousands of fake accounts and using them to place spurious orders and disrupt Uber’s...